Skolem–Mahler–Lech theorem

In additive and algebraic number theory, the Skolem–Mahler–Lech theorem states that if a sequence of numbers satisfies a linear difference equation, then with finitely many exceptions the positions at which the sequence is zero form a regularly repeating pattern. This result is named after Thoralf Skolem (who proved the theorem for sequences of rational numbers), Kurt Mahler (who proved it for sequences of algebraic numbers), and Christer Lech (who proved it for sequences whose elements belong to any field of characteristic 0). Its known proofs use p-adic analysis and are non-constructive.